The course gives an introduction to algebraic topology. The topics treated include the notion of homotopy, the fundamental group, and homology theories with the example of singular homology.

Cohomology groups, cup product, Poincaré duality theorem, homotopy groups, Whitehead theorem, Hurewicz theorem, obstruction theory (if time permits)

The aim of this class is to introduce classical tools in the study of knots and links: the group of a knot, Seifert surfaces, the Alexander module, the Alexander-Conway polynomial, the Levine-Tristram signature,... These objects are defined using methods of algebraic topology; therefore, we will assume a basic knowledge of algebraic topology.